Answer:
8.75 feet
Step by step:
Given that a 12 foot ladder leans against a building seven feet above the ground.
By using trigonometry ratio, the angle between the ladder and the ground will be
SinĂ˜ = opposite/ hypothenus
SinĂ˜ = 7 / 12
SinĂ˜ = 0.58333
Ă˜ = Sin^-1(0.58333)
Ă˜ = 35.69 degree
At what height would an 15 foot ladder touch the building if both ladders form the same angle with the ground?
Using the same trigonometric ratios
SinĂ˜ = opposite/hypothenus
Sin 35.69 = opposite/ 15
Cross multiply
Opposite = 15 Ă— sin 35.69
Opposite = 8.75 feet
Therefore, the ladder will touch the building if both ladders form the same angle with the ground at height 8.75 feet.
